Here is one, not too elegant, method to do as you wish using a single formula. However, you will have to adjust your options to enable the use of circular references. This formula assumes the non-repeating numbers 1-10 will be returned in cells A1:A10.
For Excel 2003, and prior:
Go to Tools > Options and select the Calculation tab. Check the 'Iteration' checkbox. Click 'OK'.
For Excel 2007/2010:
Go to File > Options and select the Formulas menu item.
Place a check mark in 'Enable iterative calculation' checkbox. Click 'OK'.
In cell A1, enter the formula:
Fill the formula down through cell A10.
Note: This formula will not recalculate when the Calculate event occurs, i.e. pressing F9. To create a new list of numbers in A1:A10, simply select cell A1 and drag the formula down through A10 again. Like I said, not too elegant. However, it does avoid VBA and other cells.